// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
#define EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H

namespace Eigen {

/** \internal
 *
 * \class TensorIntDiv
 * \ingroup CXX11_Tensor_Module
 *
 * \brief Fast integer division by a constant.
 *
 * See the paper from Granlund and Montgomery for explanation.
 *   (at https://doi.org/10.1145/773473.178249)
 *
 * \sa Tensor
 */

namespace internal {

namespace {

// Note: result is undefined if val == 0
template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE typename internal::enable_if<sizeof(T) == 4, int>::type
count_leading_zeros(const T val)
{
#ifdef EIGEN_GPU_COMPILE_PHASE
	return __clz(val);
#elif defined(SYCL_DEVICE_ONLY)
	return cl::sycl::clz(val);
#elif EIGEN_COMP_MSVC
	unsigned long index;
	_BitScanReverse(&index, val);
	return 31 - index;
#else
	EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);
	return __builtin_clz(static_cast<uint32_t>(val));
#endif
}

template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE typename internal::enable_if<sizeof(T) == 8, int>::type
count_leading_zeros(const T val)
{
#ifdef EIGEN_GPU_COMPILE_PHASE
	return __clzll(val);
#elif defined(SYCL_DEVICE_ONLY)
	return static_cast<int>(cl::sycl::clz(val));
#elif EIGEN_COMP_MSVC && EIGEN_ARCH_x86_64
	unsigned long index;
	_BitScanReverse64(&index, val);
	return 63 - index;
#elif EIGEN_COMP_MSVC
	// MSVC's _BitScanReverse64 is not available for 32bits builds.
	unsigned int lo = (unsigned int)(val & 0xffffffff);
	unsigned int hi = (unsigned int)((val >> 32) & 0xffffffff);
	int n;
	if (hi == 0)
		n = 32 + count_leading_zeros<unsigned int>(lo);
	else
		n = count_leading_zeros<unsigned int>(hi);
	return n;
#else
	EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);
	return __builtin_clzll(static_cast<uint64_t>(val));
#endif
}

template<typename T>
struct UnsignedTraits
{
	typedef typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type type;
};

template<typename T>
struct DividerTraits
{
	typedef typename UnsignedTraits<T>::type type;
	static const int N = sizeof(T) * 8;
};

template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t
muluh(const uint32_t a, const T b)
{
#if defined(EIGEN_GPU_COMPILE_PHASE)
	return __umulhi(a, b);
#elif defined(SYCL_DEVICE_ONLY)
	return cl::sycl::mul_hi(a, static_cast<uint32_t>(b));
#else
	return (static_cast<uint64_t>(a) * b) >> 32;
#endif
}

template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t
muluh(const uint64_t a, const T b)
{
#if defined(EIGEN_GPU_COMPILE_PHASE)
	return __umul64hi(a, b);
#elif defined(SYCL_DEVICE_ONLY)
	return cl::sycl::mul_hi(a, static_cast<uint64_t>(b));
#elif EIGEN_HAS_BUILTIN_INT128
	__uint128_t v = static_cast<__uint128_t>(a) * static_cast<__uint128_t>(b);
	return static_cast<uint64_t>(v >> 64);
#else
	return (TensorUInt128<static_val<0>, uint64_t>(a) * TensorUInt128<static_val<0>, uint64_t>(b)).upper();
#endif
}

template<int N, typename T>
struct DividerHelper
{
	static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t computeMultiplier(const int log_div, const T divider)
	{
		EIGEN_STATIC_ASSERT(N == 32, YOU_MADE_A_PROGRAMMING_MISTAKE);
		return static_cast<uint32_t>((static_cast<uint64_t>(1) << (N + log_div)) / divider -
									 (static_cast<uint64_t>(1) << N) + 1);
	}
};

template<typename T>
struct DividerHelper<64, T>
{
	static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t computeMultiplier(const int log_div, const T divider)
	{
#if EIGEN_HAS_BUILTIN_INT128 && !defined(EIGEN_GPU_COMPILE_PHASE) && !defined(SYCL_DEVICE_ONLY)
		return static_cast<uint64_t>((static_cast<__uint128_t>(1) << (64 + log_div)) /
										 static_cast<__uint128_t>(divider) -
									 (static_cast<__uint128_t>(1) << 64) + 1);
#else
		const uint64_t shift = 1ULL << log_div;
		TensorUInt128<uint64_t, uint64_t> result =
			TensorUInt128<uint64_t, static_val<0>>(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider) -
			TensorUInt128<static_val<1>, static_val<0>>(1, 0) + TensorUInt128<static_val<0>, static_val<1>>(1);
		return static_cast<uint64_t>(result);
#endif
	}
};
}

template<typename T, bool div_gt_one = false>
struct TensorIntDivisor
{
  public:
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor()
	{
		multiplier = 0;
		shift1 = 0;
		shift2 = 0;
	}

	// Must have 0 < divider < 2^31. This is relaxed to
	// 0 < divider < 2^63 when using 64-bit indices on platforms that support
	// the __uint128_t type.
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor(const T divider)
	{
		const int N = DividerTraits<T>::N;
		eigen_assert(static_cast<typename UnsignedTraits<T>::type>(divider) < NumTraits<UnsignedType>::highest() / 2);
		eigen_assert(divider > 0);

		// fast ln2
		const int leading_zeros = count_leading_zeros(static_cast<UnsignedType>(divider));
		int log_div = N - leading_zeros;
		// if divider is a power of two then log_div is 1 more than it should be.
		if ((static_cast<typename UnsignedTraits<T>::type>(1) << (log_div - 1)) ==
			static_cast<typename UnsignedTraits<T>::type>(divider))
			log_div--;

		multiplier = DividerHelper<N, T>::computeMultiplier(log_div, divider);
		shift1 = log_div > 1 ? 1 : log_div;
		shift2 = log_div > 1 ? log_div - 1 : 0;
	}

	// Must have 0 <= numerator. On platforms that don't support the __uint128_t
	// type numerator should also be less than 2^32-1.
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T divide(const T numerator) const
	{
		eigen_assert(static_cast<typename UnsignedTraits<T>::type>(numerator) < NumTraits<UnsignedType>::highest() / 2);
		// eigen_assert(numerator >= 0); // this is implicitly asserted by the line above

		UnsignedType t1 = muluh(multiplier, numerator);
		UnsignedType t = (static_cast<UnsignedType>(numerator) - t1) >> shift1;
		return (t1 + t) >> shift2;
	}

  private:
	typedef typename DividerTraits<T>::type UnsignedType;
	UnsignedType multiplier;
	int32_t shift1;
	int32_t shift2;
};

// Optimized version for signed 32 bit integers.
// Derived from Hacker's Delight.
// Only works for divisors strictly greater than one
template<>
class TensorIntDivisor<int32_t, true>
{
  public:
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor()
	{
		magic = 0;
		shift = 0;
	}
	// Must have 2 <= divider
	EIGEN_DEVICE_FUNC TensorIntDivisor(int32_t divider)
	{
		eigen_assert(divider >= 2);
		calcMagic(divider);
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE int divide(const int32_t n) const
	{
#ifdef EIGEN_GPU_COMPILE_PHASE
		return (__umulhi(magic, n) >> shift);
#elif defined(SYCL_DEVICE_ONLY)
		return (cl::sycl::mul_hi(magic, static_cast<uint32_t>(n)) >> shift);
#else
		uint64_t v = static_cast<uint64_t>(magic) * static_cast<uint64_t>(n);
		return (static_cast<uint32_t>(v >> 32) >> shift);
#endif
	}

  private:
	// Compute the magic numbers. See Hacker's Delight section 10 for an in
	// depth explanation.
	EIGEN_DEVICE_FUNC void calcMagic(int32_t d)
	{
		const unsigned two31 = 0x80000000; // 2**31.
		unsigned ad = d;
		unsigned t = two31 + (ad >> 31);
		unsigned anc = t - 1 - t % ad;	// Absolute value of nc.
		int p = 31;						// Init. p.
		unsigned q1 = two31 / anc;		// Init. q1 = 2**p/|nc|.
		unsigned r1 = two31 - q1 * anc; // Init. r1 = rem(2**p, |nc|).
		unsigned q2 = two31 / ad;		// Init. q2 = 2**p/|d|.
		unsigned r2 = two31 - q2 * ad;	// Init. r2 = rem(2**p, |d|).
		unsigned delta = 0;
		do {
			p = p + 1;
			q1 = 2 * q1;	 // Update q1 = 2**p/|nc|.
			r1 = 2 * r1;	 // Update r1 = rem(2**p, |nc|).
			if (r1 >= anc) { // (Must be an unsigned
				q1 = q1 + 1; // comparison here).
				r1 = r1 - anc;
			}
			q2 = 2 * q2;	 // Update q2 = 2**p/|d|.
			r2 = 2 * r2;	 // Update r2 = rem(2**p, |d|).
			if (r2 >= ad) {	 // (Must be an unsigned
				q2 = q2 + 1; // comparison here).
				r2 = r2 - ad;
			}
			delta = ad - r2;
		} while (q1 < delta || (q1 == delta && r1 == 0));

		magic = (unsigned)(q2 + 1);
		shift = p - 32;
	}

	uint32_t magic;
	int32_t shift;
};

template<typename T, bool div_gt_one>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T
operator/(const T& numerator, const TensorIntDivisor<T, div_gt_one>& divisor)
{
	return divisor.divide(numerator);
}

} // end namespace internal
} // end namespace Eigen

#endif // EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
